Problem: Simplify the following expression: $t = \dfrac{-10r^2 - 40r + 600}{r - 6} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ t =\dfrac{-10(r^2 + 4r - 60)}{r - 6} $ Then we factor the remaining polynomial: $r^2 + {4}r {-60} $ ${-6} + {10} = {4}$ ${-6} \times {10} = {-60}$ $ (r {-6}) (r + {10}) $ This gives us a factored expression: $\dfrac{-10(r {-6}) (r + {10})}{r - 6}$ We can divide the numerator and denominator by $(r + 6)$ on condition that $r \neq 6$ Therefore $t = -10(r + 10); r \neq 6$